Recumbent shorts have little or no padding.

Hostel Shoppe used to sell the excellent Volae shorts, but no longer list them. These are 8-panel lycra (panels cut just like regular cycling shorts) but with an extra layer of lycra where the chamois pad would normally be. http://www.hostelshoppe.com/

The Volae shorts were custom-ordered wholesale by Hostel Shoppe from Hidden Bay Sports, but that website shows no unpadded varieties. http://hiddenbaysports.com/

I prefer these shorts (for recumbent riding) but one thing to consider for upright use is that they lack a drawstring on the waist. For recumbents, keeping your pants up isn't such a problem.

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The Mt Borah shorts that Hostel Shoppe shows are also essentially unpadded, but they are "MTB-style" shorts (-a regular-looking outer shell with an inner, tight-fitting liner sewn in at the waist-). The Mt Borahs I own do have a drawstring waist.

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Kucharik lists some recumbent-specific shorts with a layer of coolmax instead of chamois. I dunno if they have a drawstring or not, I never owned any, you'd have to email and ask. http://www.kucharik.com/

I don't know any other places that sell anything like unpadded shorts that is bicycle-specific. Hostel Shoppe is the biggest/most comprehensive online recumbent store around, at least in the USA.

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I've also heard of people using exercise/compression shorts, as well as rowing shorts (in particular, SewSporty is a common source mentioned for rowing shorts). These can be bought cheap and can work very well on a recumbent seat, but I don't know about an upright saddle.
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